Most problems have moved to:
| http://electron9.phys.utk.edu/phys513/Modules/module_7.htm |
| http://electron9.phys.utk.edu/phys513/Modules/module_8.htm |
| Problem: A fixed center of force at the origin repels a particle of
mass m with a force whose magnitude is k/r2. The particles
kinetic energy at a large distance from the origin is E0 and may have
values between 0 and ¥. In the absence of a force the particle
would move along the line given by y = 0, x = b. With the assumed force, what will be
the distance of closest approach, a, to the origin when the particle is treated
relativistically? Show that your result reduces to the obvious answer if k = 0, that a =k/E0
for a head-on collision where b = 0 and that your result reduces to the
nonrelativistic result
|
| Problem: A relativistic particle is launched at the origin (0,0) with initial momentum P(0) = (Px(0),Py(0)), with Px(0) > 0 and Py(0) > 0, and is subject to a constant force pointing in the negative y direction. (a) Solve the
equations of motion. NOTE: Give all answers for the laboratory frame.
| ||
| Problem: Consider a thin rod of length d and constant linear mass density s. The rod is assumed to remain straight at all times, and to be unstretchable. The rod is rotated about its center such that the endpoints moving tangentially at v ~ c. Show that the total energy of the rod E and its angular momentum J are
related by
|
when E0
<< mc2.
